The purpose of this project is to measure forces and moments from existing orthodontic applicances and to evaluate the force systems produced. New appliances and modifications of existing appliances will be designed and tested to optimize the force system. Both material properties and design parameters will be studied. Forces will be measured in uniplanar and three -dimensional activations; with rigid and sliding supports; over small and large deflections; and between two teeth or larger multiple tooth units. Beam theory capable of handling both large and small deflections in three dimensional space has been developed. The analytical methods can determine the force system from a given appliance if the activation is known, or given the appliance, the activations required for a desired force system can be determined. The program can be used for simple wires, wires with configurations such as loops and multiple beams. Experimental force transducers have been developed which measure simultaneous forces and couples at an orthodontic bracket in three dimensions and other unique transducers have been developed to measure forces and moments concurrent with increasing and decreasing activations. The force system of a number of appliance modalities will be studied. These include "straight wires" with or without loops, multiplanar loading of headgears, optimizing lingual and transpalatal arch designs, torsional devices, multiple cross section components, "lingual orthodontics" and retraction mechanisms. Studies of relevant mechanical properties of orthodontic wires will emphasize the determination of maximum bending moments, the modulus of rigidity by torsional loading, the properties of multi-strand wires, and studies of formability.